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Learning the combat rules

I think I'm just dense, but I'm having some trouble figuring something to do with attack bonuses. And weapons proficiencies. And other stuff.

I haven't been in the game(s) for awhile and the amount of information I need to absorb before I start running a game is a bit daunting.

So, question the first.

When a character's class lists her weapon proficiencies, in most (but not all) cases they list categories (simple melee, military ranged, etc). Does that mean that characters of that class are proficient in all weapons of that category, thus gaining the proficiency bonus listed for the individual weapons in the tables at PHB pp 218-219?

Question the second.

I think I might lack the vocabulary to state this one succinctly (unlike the masterpiece of brevity that was question #1 ). It has to do with which bonuses apply to attacks (which I gather now just means "to hit," not both "to hit" and "damage"), which to damage, and how they relate to powers.

Say I have a first level fighter who has a Strength score of 18. He's got the Fighter Weapon Talent that gives him a +1 to attack using two-handed weapons and specialization in his greataxe through his class specialization in military melee weapons.

Now, the big thing is this. How do bonuses other than ability come in to play when using an Exploit, like Sure Strike for example? Sure Strike's description says that the attack is figured on Str +2 vs. AC and on a hit damage is 1[W].

Does that mean that if my fighter swings at foe using his ability, he rolls d20 and adds 6, and on a hit he rolls 1d12?

Because that's not as good as just using his basic attack with it's d20+7 to hit and d12+4 to damage, is it? With all the emphasis placed on abilities, it seems odd that the basic attacks would be better than the abilities for the martial types.

Anyway, like I said, I'm pretty sure I'm just missing some crucial paragraph or something. I wish they'd included more examples of combat, but I suppose the book's pretty danged long as it is.

Str + 2 vs AC means that strength is the attribute that you should look at. 1/2 level is always added, and if the power contains the weapon keyword, then his weapon proficiency is added and enhancements bonuses from magic weapons are also added. I also believe that he also would get his feat bonus for the to hit.

As for the damage being 1[W] instead of 1[W]+strength, that's the sacrifice he makes to get that +2 to hit.